### A one-dimensional dynamical system with random switching

- Series
- SIAM Student Seminar
- Time
- Friday, March 18, 2011 - 13:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 246
- Speaker
- Tobias Hurth – School of Mathematics, Georgia Tech

We will study a simple dynamical system with two driving vector
fields on the unit interval. The driving vector fields point to opposite
directions, and we will follow the trajectory induced by one vector field
for a random, exponentially distributed, amount of time before switching to
the regime of the other one. Thanks to the simplicity of the system, we
obtain an explicit formula for its invariant density. Basically exploiting
analytic properties of this density, we derive versions of the law of large
numbers, the central limit theorem and the large deviations principle for
our system. If time permits, we will also discuss some ideas on how to prove
existence of invariant densities, both in our one-dimensional setting and
for more general systems with random switching. The talk will rely to a
large extent on my Master's thesis I wrote last year under the guidance and
supervision of Yuri Bakhtin.